A poll reported that 66% of adults were satisfied with the job the major airlines were doing. Suppose 20 adults are selected at random and the number who are satisfied is recorded.

The probability that exactly 12 are satisfied with the airlines is

0.5640

Step-by-step explanation:

n = 12 (number of adults)

p = 0.65 (probability that an adult is satisfied with the job the major airlines were doing.

x = number of adults out of 11 who were satisfied.

a)

P (x = 5) = 11C5 (0.65) ^5 (0.35) ^6 = 0.0986

b)

P (x < 3) = P (x=0) + P (x=1) + P (x=2)

P (x = 0) = 11C0 (0.65) ^0 (0.35) ^11 = 0.0000

P (x = 1) = 11C1 (0.65) ^1 (0.35) ^10 = 0.0002

P (x = 2) = 11C2 (0.65) ^2 (0.35) ^9 = 0.0018

Add: P (x < 3) = 0.0020

c)

P (x ≥ 8) = P (x=8) + P (x=9) + P (x=10) + P (x=11)

P (x = 8) = 11C8 (0.65) ^8 (0.35) ^3 = 0.2254

P (x = 9) = 11C9 (0.65) ^9 (0.35) ^2 = 0.1395

P (x = 10) = 11C10 (0.65) ^10 (0.35) ^1 = 0.0518

P (x = 11) = 11C11 (0.65) ^11 (0.35) ^0 = 0.0087

add:

P (x ≥ 8) = 0.4254

d)

P (x=4) + P (x=5) + P (x=6) + P (x=7)

P (x = 4) = 11C4 (0.65) ^4 (0.35) ^7 = 0.0379

P (x = 5) = 11C5 (0.65) ^5 (0.35) ^6 = 0.0985

P (x = 6) = 11C6 (0.65) ^6 (0.35) ^5 = 0.1830

P (x = 7) = 11C7 (0.65) ^7 (0.35) ^4 = 0.2428

Add: 0.5640